Marni, of course you can do this. I think a lot of what determines whether or not we can do something takes place between our ears. If you think you can do a 5K then you can. I'm not implying that just by thinking it you can suddenly & miraculously do it. Of course you have to train and prepare, but if you do those things you will run 5K. No doubt.
I used the Couch to 5K (C25k) plan to train and build up to running. It was great. I was just under 200 lbs.
So keep going and you will do it. I have full confidence in you.
"Opportunity is missed by most people because it is dressed in overalls & looks like work" - Thomas Edison